%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV465^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:39:33 AM UTC 2026
% Result : Theorem 0.19s 0.32s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 8
% Syntax : Number of formulae : 96 ( 18 unt; 0 typ; 6 def)
% Number of atoms : 583 ( 128 equ; 0 cnn)
% Maximal formula atoms : 5 ( 6 avg)
% Number of connectives : 888 ( 77 ~; 119 |; 10 &; 625 @)
% ( 6 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 47 ( 47 >; 0 *; 0 +; 0 <<)
% Number of symbols : 28 ( 23 usr; 12 con; 0-5 aty)
% ( 14 !!; 4 ??; 0 @@+; 0 @@-)
% Number of variables : 162 ( 0 sgn 129 !; 7 ?; 162 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_6,type,
sK0: $tType ).
thf(type_def_7,type,
sK1: $tType ).
thf(func_def_0,type,
'const/sets/IN':
!>[X0: $tType] : ( X0 > ( X0 > $o ) > $o ) ).
thf(func_def_1,type,
'const/sets/IMAGE':
!>[X0: $tType,X1: $tType] : ( ( X0 > X1 ) > ( X0 > $o ) > X1 > $o ) ).
thf(func_def_3,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_4,type,
vAND: $o > $o > $o ).
thf(func_def_5,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_6,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_7,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_8,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_9,type,
vIMP: $o > $o > $o ).
thf(func_def_10,type,
sK2: sK0 > $o ).
thf(func_def_11,type,
sK3: sK1 > sK0 ).
thf(func_def_12,type,
sK4: sK1 > $o ).
thf(func_def_15,type,
sK5: sK0 ).
thf(func_def_16,type,
sK6: sK1 ).
thf(func_def_17,type,
sK7:
!>[X0: $tType,X1: $tType] : ( ( X1 > $o ) > ( X1 > X0 ) > X0 > X1 ) ).
thf(func_def_19,type,
db1:
!>[X0: $tType] : X0 ).
thf(f1,axiom,
! [X1: $tType,X0: $tType,X2: X1,X3: X0 > $o,X4: X0 > X1] :
( ( 'const/sets/IN' @ X1 @ X2 @ ( 'const/sets/IMAGE' @ X0 @ X1 @ X4 @ X3 ) )
= ( ? [X5: X0] :
( ( 'const/sets/IN' @ X0 @ X5 @ X3 )
& ( X2
= ( X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/IN_IMAGE_') ).
thf(f2,conjecture,
! [X0: $tType,X1: $tType,X2: X0 > $o,X3: X1 > X0,X4: X1 > $o,X5: X0] :
( ( ( 'const/sets/IN' @ X0 @ X5 @ ( 'const/sets/IMAGE' @ X1 @ X0 @ X3 @ X4 ) )
=> ( X2 @ X5 ) )
= ( ! [X5: X1] :
( ( 'const/sets/IN' @ X1 @ X5 @ X4 )
=> ( X2 @ ( X3 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/FORALL_IN_IMAGE_') ).
thf(f3,negated_conjecture,
~ ! [X0: $tType,X1: $tType,X2: X0 > $o,X3: X1 > X0,X4: X1 > $o,X5: X0] :
( ( ( 'const/sets/IN' @ X0 @ X5 @ ( 'const/sets/IMAGE' @ X1 @ X0 @ X3 @ X4 ) )
=> ( X2 @ X5 ) )
= ( ! [X5: X1] :
( ( 'const/sets/IN' @ X1 @ X5 @ X4 )
=> ( X2 @ ( X3 @ X5 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f4,plain,
! [X0: $tType,X1: $tType,X2: X0,X3: X1 > $o,X4: X1 > X0] :
( ( 'const/sets/IN' @ X0 @ X2 @ ( 'const/sets/IMAGE' @ X1 @ X0 @ X4 @ X3 ) )
= ( ? [X5: X1] :
( ( 'const/sets/IN' @ X1 @ X5 @ X3 )
& ( ( X4 @ X5 )
= X2 ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f5,plain,
! [X0: $tType,X1: $tType,X2: X0,X3: X1 > $o,X4: X1 > X0] :
( ( 'const/sets/IN' @ X0 @ X2 @ ( 'const/sets/IMAGE' @ X1 @ X0 @ X4 @ X3 ) )
= ( ?? @ X1
@ ^ [Y0: X1] :
( ( ( X4 @ Y0 )
= X2 )
& ( 'const/sets/IN' @ X1 @ Y0 @ X3 ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f6,plain,
~ ! [X0: $tType,X1: $tType,X2: X0 > $o,X3: X1 > X0,X4: X1 > $o,X5: X0] :
( ( ( 'const/sets/IN' @ X0 @ X5 @ ( 'const/sets/IMAGE' @ X1 @ X0 @ X3 @ X4 ) )
=> ( X2 @ X5 ) )
= ( ! [X6: X1] :
( ( 'const/sets/IN' @ X1 @ X6 @ X4 )
=> ( X2 @ ( X3 @ X6 ) ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f7,plain,
~ ! [X0: $tType,X1: $tType,X2: X0 > $o,X3: X1 > X0,X4: X1 > $o] :
( ( !! @ X0
@ ^ [Y0: X0] :
( ( 'const/sets/IN' @ X0 @ Y0 @ ( 'const/sets/IMAGE' @ X1 @ X0 @ X3 @ X4 ) )
=> ( X2 @ Y0 ) ) )
= ( !! @ X1
@ ^ [Y0: X1] :
( ( 'const/sets/IN' @ X1 @ Y0 @ X4 )
=> ( X2 @ ( X3 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
? [X0: $tType,X1: $tType,X2: X0 > $o,X3: X1 > X0,X4: X1 > $o] :
( ( !! @ X0
@ ^ [Y0: X0] :
( ( 'const/sets/IN' @ X0 @ Y0 @ ( 'const/sets/IMAGE' @ X1 @ X0 @ X3 @ X4 ) )
=> ( X2 @ Y0 ) ) )
!= ( !! @ X1
@ ^ [Y0: X1] :
( ( 'const/sets/IN' @ X1 @ Y0 @ X4 )
=> ( X2 @ ( X3 @ Y0 ) ) ) ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f9,plain,
( ( !! @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ ( 'const/sets/IMAGE' @ sK1 @ sK0 @ sK3 @ sK4 ) )
=> ( sK2 @ Y0 ) ) )
!= ( !! @ sK1
@ ^ [Y0: sK1] :
( ( 'const/sets/IN' @ sK1 @ Y0 @ sK4 )
=> ( sK2 @ ( sK3 @ Y0 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4)],[f8]) ).
thf(f10,plain,
! [X1: $tType,X0: $tType,X2: X0,X3: X1 > $o,X4: X1 > X0] :
( ( 'const/sets/IN' @ X0 @ X2 @ ( 'const/sets/IMAGE' @ X1 @ X0 @ X4 @ X3 ) )
= ( ?? @ X1
@ ^ [Y0: X1] :
( ( ( X4 @ Y0 )
= X2 )
& ( 'const/sets/IN' @ X1 @ Y0 @ X3 ) ) ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f11,plain,
( ( !! @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ ( 'const/sets/IMAGE' @ sK1 @ sK0 @ sK3 @ sK4 ) )
=> ( sK2 @ Y0 ) ) )
!= ( !! @ sK1
@ ^ [Y0: sK1] :
( ( 'const/sets/IN' @ sK1 @ Y0 @ sK4 )
=> ( sK2 @ ( sK3 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f14,plain,
( ( ( !! @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ ( 'const/sets/IMAGE' @ sK1 @ sK0 @ sK3 @ sK4 ) )
=> ( sK2 @ Y0 ) ) )
= $true )
| ( ( !! @ sK1
@ ^ [Y0: sK1] :
( ( 'const/sets/IN' @ sK1 @ Y0 @ sK4 )
=> ( sK2 @ ( sK3 @ Y0 ) ) ) )
= $true ) ),
inference(xor_proxy_clausification,[],[f11]) ).
thf(f15,plain,
( ( ( !! @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ ( 'const/sets/IMAGE' @ sK1 @ sK0 @ sK3 @ sK4 ) )
=> ( sK2 @ Y0 ) ) )
= $false )
| ( ( !! @ sK1
@ ^ [Y0: sK1] :
( ( 'const/sets/IN' @ sK1 @ Y0 @ sK4 )
=> ( sK2 @ ( sK3 @ Y0 ) ) ) )
= $false ) ),
inference(xor_proxy_clausification,[],[f11]) ).
thf(f16,plain,
( ( $false
= ( ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ ( 'const/sets/IMAGE' @ sK1 @ sK0 @ sK3 @ sK4 ) )
=> ( sK2 @ Y0 ) )
@ sK5 ) )
| ( ( !! @ sK1
@ ^ [Y0: sK1] :
( ( 'const/sets/IN' @ sK1 @ Y0 @ sK4 )
=> ( sK2 @ ( sK3 @ Y0 ) ) ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f15]) ).
thf(f17,plain,
( ( $false
= ( ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ ( 'const/sets/IMAGE' @ sK1 @ sK0 @ sK3 @ sK4 ) )
=> ( sK2 @ Y0 ) )
@ sK5 ) )
| ( $false
= ( ^ [Y0: sK1] :
( ( 'const/sets/IN' @ sK1 @ Y0 @ sK4 )
=> ( sK2 @ ( sK3 @ Y0 ) ) )
@ sK6 ) ) ),
inference(sigma_proxy_clausification,[],[f16]) ).
thf(f18,plain,
( ( $false
= ( ( 'const/sets/IN' @ sK0 @ sK5 @ ( 'const/sets/IMAGE' @ sK1 @ sK0 @ sK3 @ sK4 ) )
=> ( sK2 @ sK5 ) ) )
| ( $false
= ( ( 'const/sets/IN' @ sK1 @ sK6 @ sK4 )
=> ( sK2 @ ( sK3 @ sK6 ) ) ) ) ),
inference(beta-eta_normalization,[],[f17]) ).
thf(f19,plain,
( ( $false
= ( sK2 @ sK5 ) )
| ( $false
= ( ( 'const/sets/IN' @ sK1 @ sK6 @ sK4 )
=> ( sK2 @ ( sK3 @ sK6 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f18]) ).
thf(f20,plain,
( ( $true
= ( 'const/sets/IN' @ sK0 @ sK5 @ ( 'const/sets/IMAGE' @ sK1 @ sK0 @ sK3 @ sK4 ) ) )
| ( $false
= ( ( 'const/sets/IN' @ sK1 @ sK6 @ sK4 )
=> ( sK2 @ ( sK3 @ sK6 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f18]) ).
thf(f21,plain,
( ( $true
= ( 'const/sets/IN' @ sK0 @ sK5 @ ( 'const/sets/IMAGE' @ sK1 @ sK0 @ sK3 @ sK4 ) ) )
| ( $false
= ( sK2 @ ( sK3 @ sK6 ) ) ) ),
inference(imp_proxy_clausification,[],[f20]) ).
thf(f22,plain,
( ( $true
= ( 'const/sets/IN' @ sK0 @ sK5 @ ( 'const/sets/IMAGE' @ sK1 @ sK0 @ sK3 @ sK4 ) ) )
| ( $true
= ( 'const/sets/IN' @ sK1 @ sK6 @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f20]) ).
thf(f23,plain,
( ( $false
= ( sK2 @ sK5 ) )
| ( $false
= ( sK2 @ ( sK3 @ sK6 ) ) ) ),
inference(imp_proxy_clausification,[],[f19]) ).
thf(f24,plain,
( ( $false
= ( sK2 @ sK5 ) )
| ( $true
= ( 'const/sets/IN' @ sK1 @ sK6 @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f19]) ).
thf(f25,plain,
! [X1: sK0] :
( ( $true
= ( ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ ( 'const/sets/IMAGE' @ sK1 @ sK0 @ sK3 @ sK4 ) )
=> ( sK2 @ Y0 ) )
@ X1 ) )
| ( ( !! @ sK1
@ ^ [Y0: sK1] :
( ( 'const/sets/IN' @ sK1 @ Y0 @ sK4 )
=> ( sK2 @ ( sK3 @ Y0 ) ) ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f14]) ).
thf(f26,plain,
! [X2: sK1,X1: sK0] :
( ( $true
= ( ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ ( 'const/sets/IMAGE' @ sK1 @ sK0 @ sK3 @ sK4 ) )
=> ( sK2 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: sK1] :
( ( 'const/sets/IN' @ sK1 @ Y0 @ sK4 )
=> ( sK2 @ ( sK3 @ Y0 ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f25]) ).
thf(f27,plain,
! [X2: sK1,X1: sK0] :
( ( $true
= ( ( 'const/sets/IN' @ sK0 @ X1 @ ( 'const/sets/IMAGE' @ sK1 @ sK0 @ sK3 @ sK4 ) )
=> ( sK2 @ X1 ) ) )
| ( $true
= ( ( 'const/sets/IN' @ sK1 @ X2 @ sK4 )
=> ( sK2 @ ( sK3 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f26]) ).
thf(f28,plain,
! [X2: sK1,X1: sK0] :
( ( $false
= ( 'const/sets/IN' @ sK0 @ X1 @ ( 'const/sets/IMAGE' @ sK1 @ sK0 @ sK3 @ sK4 ) ) )
| ( $true
= ( ( 'const/sets/IN' @ sK1 @ X2 @ sK4 )
=> ( sK2 @ ( sK3 @ X2 ) ) ) )
| ( $true
= ( sK2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f27]) ).
thf(f29,plain,
! [X2: sK1,X1: sK0] :
( ( $false
= ( 'const/sets/IN' @ sK0 @ X1 @ ( 'const/sets/IMAGE' @ sK1 @ sK0 @ sK3 @ sK4 ) ) )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK4 ) )
| ( $true
= ( sK2 @ X1 ) )
| ( $true
= ( sK2 @ ( sK3 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f28]) ).
thf(f30,plain,
! [X1: $tType,X0: $tType,X2: X0,X3: X1 > $o,X4: X1 > X0] :
( ( ( 'const/sets/IN' @ X0 @ X2 @ ( 'const/sets/IMAGE' @ X1 @ X0 @ X4 @ X3 ) )
= $true )
| ( ( ?? @ X1
@ ^ [Y0: X1] :
( ( ( X4 @ Y0 )
= X2 )
& ( 'const/sets/IN' @ X1 @ Y0 @ X3 ) ) )
= $false ) ),
inference(iff_proxy_clausification,[],[f10]) ).
thf(f31,plain,
! [X1: $tType,X0: $tType,X2: X0,X3: X1 > $o,X4: X1 > X0] :
( ( ( 'const/sets/IN' @ X0 @ X2 @ ( 'const/sets/IMAGE' @ X1 @ X0 @ X4 @ X3 ) )
= $false )
| ( ( ?? @ X1
@ ^ [Y0: X1] :
( ( ( X4 @ Y0 )
= X2 )
& ( 'const/sets/IN' @ X1 @ Y0 @ X3 ) ) )
= $true ) ),
inference(iff_proxy_clausification,[],[f10]) ).
thf(f32,plain,
! [X1: $tType,X0: $tType,X2: X0,X3: X1 > $o,X4: X1 > X0] :
( ( ( 'const/sets/IN' @ X0 @ X2 @ ( 'const/sets/IMAGE' @ X1 @ X0 @ X4 @ X3 ) )
= $false )
| ( $true
= ( ^ [Y0: X1] :
( ( ( X4 @ Y0 )
= X2 )
& ( 'const/sets/IN' @ X1 @ Y0 @ X3 ) )
@ ( sK7 @ X0 @ X1 @ X3 @ X4 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f31]) ).
thf(f33,plain,
! [X1: $tType,X0: $tType,X2: X0,X3: X1 > $o,X4: X1 > X0] :
( ( ( 'const/sets/IN' @ X0 @ X2 @ ( 'const/sets/IMAGE' @ X1 @ X0 @ X4 @ X3 ) )
= $false )
| ( $true
= ( ( ( X4 @ ( sK7 @ X0 @ X1 @ X3 @ X4 @ X2 ) )
= X2 )
& ( 'const/sets/IN' @ X1 @ ( sK7 @ X0 @ X1 @ X3 @ X4 @ X2 ) @ X3 ) ) ) ),
inference(beta-eta_normalization,[],[f32]) ).
thf(f34,plain,
! [X1: $tType,X0: $tType,X2: X0,X3: X1 > $o,X4: X1 > X0] :
( ( ( 'const/sets/IN' @ X0 @ X2 @ ( 'const/sets/IMAGE' @ X1 @ X0 @ X4 @ X3 ) )
= $false )
| ( $true
= ( 'const/sets/IN' @ X1 @ ( sK7 @ X0 @ X1 @ X3 @ X4 @ X2 ) @ X3 ) ) ),
inference(and_proxy_clausification,[],[f33]) ).
thf(f35,plain,
! [X1: $tType,X0: $tType,X2: X0,X3: X1 > $o,X4: X1 > X0] :
( ( ( 'const/sets/IN' @ X0 @ X2 @ ( 'const/sets/IMAGE' @ X1 @ X0 @ X4 @ X3 ) )
= $false )
| ( $true
= ( ( X4 @ ( sK7 @ X0 @ X1 @ X3 @ X4 @ X2 ) )
= X2 ) ) ),
inference(and_proxy_clausification,[],[f33]) ).
thf(f36,plain,
! [X1: $tType,X0: $tType,X2: X0,X3: X1 > $o,X4: X1 > X0] :
( ( ( 'const/sets/IN' @ X0 @ X2 @ ( 'const/sets/IMAGE' @ X1 @ X0 @ X4 @ X3 ) )
= $false )
| ( ( X4 @ ( sK7 @ X0 @ X1 @ X3 @ X4 @ X2 ) )
= X2 ) ),
inference(equality_proxy_clausification,[],[f35]) ).
thf(f37,plain,
! [X1: $tType,X0: $tType,X2: X0,X3: X1 > $o,X4: X1 > X0,X5: X1] :
( ( ( 'const/sets/IN' @ X0 @ X2 @ ( 'const/sets/IMAGE' @ X1 @ X0 @ X4 @ X3 ) )
= $true )
| ( $false
= ( ^ [Y0: X1] :
( ( ( X4 @ Y0 )
= X2 )
& ( 'const/sets/IN' @ X1 @ Y0 @ X3 ) )
@ X5 ) ) ),
inference(pi_proxy_clausification,[],[f30]) ).
thf(f38,plain,
! [X1: $tType,X0: $tType,X2: X0,X3: X1 > $o,X4: X1 > X0,X5: X1] :
( ( ( 'const/sets/IN' @ X0 @ X2 @ ( 'const/sets/IMAGE' @ X1 @ X0 @ X4 @ X3 ) )
= $true )
| ( $false
= ( ( ( X4 @ X5 )
= X2 )
& ( 'const/sets/IN' @ X1 @ X5 @ X3 ) ) ) ),
inference(beta-eta_normalization,[],[f37]) ).
thf(f39,plain,
! [X1: $tType,X0: $tType,X2: X0,X3: X1 > $o,X4: X1 > X0,X5: X1] :
( ( ( 'const/sets/IN' @ X0 @ X2 @ ( 'const/sets/IMAGE' @ X1 @ X0 @ X4 @ X3 ) )
= $true )
| ( ( 'const/sets/IN' @ X1 @ X5 @ X3 )
= $false )
| ( $false
= ( ( X4 @ X5 )
= X2 ) ) ),
inference(and_proxy_clausification,[],[f38]) ).
thf(f40,plain,
! [X1: $tType,X0: $tType,X2: X0,X3: X1 > $o,X4: X1 > X0,X5: X1] :
( ( ( 'const/sets/IN' @ X0 @ X2 @ ( 'const/sets/IMAGE' @ X1 @ X0 @ X4 @ X3 ) )
= $true )
| ( ( 'const/sets/IN' @ X1 @ X5 @ X3 )
= $false )
| ( ( X4 @ X5 )
!= X2 ) ),
inference(equality_proxy_clausification,[],[f39]) ).
thf(f42,definition,
( spl8_1
<=> ( $true
= ( 'const/sets/IN' @ sK1 @ sK6 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_1])],[avatar_definition]) ).
thf(f44,plain,
( ( $true
= ( 'const/sets/IN' @ sK1 @ sK6 @ sK4 ) )
| ~ spl8_1 ),
inference(avatar_component_clause,[],[f42]) ).
thf(f46,definition,
( spl8_2
<=> ( $true
= ( 'const/sets/IN' @ sK0 @ sK5 @ ( 'const/sets/IMAGE' @ sK1 @ sK0 @ sK3 @ sK4 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl8_2])],[avatar_definition]) ).
thf(f48,plain,
( ( $true
= ( 'const/sets/IN' @ sK0 @ sK5 @ ( 'const/sets/IMAGE' @ sK1 @ sK0 @ sK3 @ sK4 ) ) )
| ~ spl8_2 ),
inference(avatar_component_clause,[],[f46]) ).
thf(f49,plain,
( spl8_1
| spl8_2 ),
inference(avatar_split_clause,[],[f22,f46,f42]) ).
thf(f51,definition,
( spl8_3
<=> ( $false
= ( sK2 @ ( sK3 @ sK6 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl8_3])],[avatar_definition]) ).
thf(f53,plain,
( ( $false
= ( sK2 @ ( sK3 @ sK6 ) ) )
| ~ spl8_3 ),
inference(avatar_component_clause,[],[f51]) ).
thf(f54,plain,
( spl8_3
| spl8_2 ),
inference(avatar_split_clause,[],[f21,f46,f51]) ).
thf(f56,definition,
( spl8_4
<=> ( $false
= ( sK2 @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_4])],[avatar_definition]) ).
thf(f58,plain,
( ( $false
= ( sK2 @ sK5 ) )
| ~ spl8_4 ),
inference(avatar_component_clause,[],[f56]) ).
thf(f59,plain,
( spl8_1
| spl8_4 ),
inference(avatar_split_clause,[],[f24,f56,f42]) ).
thf(f60,plain,
( spl8_3
| spl8_4 ),
inference(avatar_split_clause,[],[f23,f56,f51]) ).
thf(f62,definition,
( spl8_5
<=> ! [X2: sK1] :
( ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK4 ) )
| ( $true
= ( sK2 @ ( sK3 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl8_5])],[avatar_definition]) ).
thf(f63,plain,
( ! [X2: sK1] :
( ( $false
= ( 'const/sets/IN' @ sK1 @ X2 @ sK4 ) )
| ( $true
= ( sK2 @ ( sK3 @ X2 ) ) ) )
| ~ spl8_5 ),
inference(avatar_component_clause,[],[f62]) ).
thf(f65,definition,
( spl8_6
<=> ! [X1: sK0] :
( ( $false
= ( 'const/sets/IN' @ sK0 @ X1 @ ( 'const/sets/IMAGE' @ sK1 @ sK0 @ sK3 @ sK4 ) ) )
| ( $true
= ( sK2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl8_6])],[avatar_definition]) ).
thf(f66,plain,
( ! [X1: sK0] :
( ( $false
= ( 'const/sets/IN' @ sK0 @ X1 @ ( 'const/sets/IMAGE' @ sK1 @ sK0 @ sK3 @ sK4 ) ) )
| ( $true
= ( sK2 @ X1 ) ) )
| ~ spl8_6 ),
inference(avatar_component_clause,[],[f65]) ).
thf(f67,plain,
( spl8_5
| spl8_6 ),
inference(avatar_split_clause,[],[f29,f65,f62]) ).
thf(f103,plain,
( ( $true = $false )
| ( sK5
= ( sK3 @ ( sK7 @ sK0 @ sK1 @ sK4 @ sK3 @ sK5 ) ) )
| ~ spl8_2 ),
inference(constrained_superposition,[],[f48,f36]) ).
thf(f147,plain,
( ( sK5
= ( sK3 @ ( sK7 @ sK0 @ sK1 @ sK4 @ sK3 @ sK5 ) ) )
| ~ spl8_2 ),
inference(trivial_inequality_removal,[],[f103]) ).
thf(f186,plain,
( ! [X0: $tType,X2: X0,X1: sK1 > X0] :
( ( $true = $false )
| ( $true
= ( sK2 @ ( sK3 @ ( sK7 @ X0 @ sK1 @ sK4 @ X1 @ X2 ) ) ) )
| ( $false
= ( 'const/sets/IN' @ X0 @ X2 @ ( 'const/sets/IMAGE' @ sK1 @ X0 @ X1 @ sK4 ) ) ) )
| ~ spl8_5 ),
inference(constrained_superposition,[],[f63,f34]) ).
thf(f193,plain,
( ! [X0: $tType,X2: X0,X1: sK1 > X0] :
( ( $false
= ( 'const/sets/IN' @ X0 @ X2 @ ( 'const/sets/IMAGE' @ sK1 @ X0 @ X1 @ sK4 ) ) )
| ( $true
= ( sK2 @ ( sK3 @ ( sK7 @ X0 @ sK1 @ sK4 @ X1 @ X2 ) ) ) ) )
| ~ spl8_5 ),
inference(trivial_inequality_removal,[],[f186]) ).
thf(f282,plain,
( ( $true = $false )
| ( $true
= ( sK2 @ ( sK3 @ ( sK7 @ sK0 @ sK1 @ sK4 @ sK3 @ sK5 ) ) ) )
| ~ spl8_2
| ~ spl8_5 ),
inference(constrained_superposition,[],[f193,f48]) ).
thf(f295,plain,
( ( $true
= ( sK2 @ ( sK3 @ ( sK7 @ sK0 @ sK1 @ sK4 @ sK3 @ sK5 ) ) ) )
| ~ spl8_2
| ~ spl8_5 ),
inference(trivial_inequality_removal,[],[f282]) ).
thf(f301,plain,
( ( $true
= ( sK2 @ sK5 ) )
| ~ spl8_2
| ~ spl8_5 ),
inference(forward_demodulation,[],[f295,f147]) ).
thf(f305,plain,
( ( $true = $false )
| ~ spl8_2
| ~ spl8_4
| ~ spl8_5 ),
inference(forward_demodulation,[],[f301,f58]) ).
thf(f306,plain,
( $false
| ~ spl8_2
| ~ spl8_4
| ~ spl8_5 ),
inference(trivial_inequality_removal,[],[f305]) ).
thf(f307,plain,
( ~ spl8_2
| ~ spl8_4
| ~ spl8_5 ),
inference(avatar_contradiction_clause,[],[f306]) ).
thf(f314,plain,
( ( $true = $false )
| ( $true
= ( sK2 @ sK5 ) )
| ~ spl8_2
| ~ spl8_6 ),
inference(constrained_superposition,[],[f66,f48]) ).
thf(f317,plain,
( ! [X0: sK0,X1: sK1] :
( ( $true = $false )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X1 @ sK4 ) )
| ( ( sK3 @ X1 )
!= X0 )
| ( $true
= ( sK2 @ X0 ) ) )
| ~ spl8_6 ),
inference(constrained_superposition,[],[f40,f66]) ).
thf(f322,plain,
( ! [X0: sK0,X1: sK1] :
( ( ( sK3 @ X1 )
!= X0 )
| ( $false
= ( 'const/sets/IN' @ sK1 @ X1 @ sK4 ) )
| ( $true
= ( sK2 @ X0 ) ) )
| ~ spl8_6 ),
inference(trivial_inequality_removal,[],[f317]) ).
thf(f325,plain,
( ( $true
= ( sK2 @ sK5 ) )
| ~ spl8_2
| ~ spl8_6 ),
inference(trivial_inequality_removal,[],[f314]) ).
thf(f335,plain,
( ( $true = $false )
| ~ spl8_2
| ~ spl8_4
| ~ spl8_6 ),
inference(forward_demodulation,[],[f325,f58]) ).
thf(f336,plain,
( $false
| ~ spl8_2
| ~ spl8_4
| ~ spl8_6 ),
inference(trivial_inequality_removal,[],[f335]) ).
thf(f337,plain,
( ~ spl8_2
| ~ spl8_4
| ~ spl8_6 ),
inference(avatar_contradiction_clause,[],[f336]) ).
thf(f390,plain,
( ( $true = $false )
| ( $true
= ( sK2 @ ( sK3 @ sK6 ) ) )
| ~ spl8_1
| ~ spl8_5 ),
inference(constrained_superposition,[],[f44,f63]) ).
thf(f397,plain,
( ( $true
= ( sK2 @ ( sK3 @ sK6 ) ) )
| ~ spl8_1
| ~ spl8_5 ),
inference(trivial_inequality_removal,[],[f390]) ).
thf(f402,plain,
( ( $true = $false )
| ~ spl8_1
| ~ spl8_3
| ~ spl8_5 ),
inference(forward_demodulation,[],[f397,f53]) ).
thf(f403,plain,
( $false
| ~ spl8_1
| ~ spl8_3
| ~ spl8_5 ),
inference(trivial_inequality_removal,[],[f402]) ).
thf(f404,plain,
( ~ spl8_1
| ~ spl8_3
| ~ spl8_5 ),
inference(avatar_contradiction_clause,[],[f403]) ).
thf(f443,plain,
( ! [X0: sK1] :
( ( $false
= ( 'const/sets/IN' @ sK1 @ X0 @ sK4 ) )
| ( $true
= ( sK2 @ ( sK3 @ X0 ) ) ) )
| ~ spl8_6 ),
inference(equality_resolution,[],[f322]) ).
thf(f444,plain,
( spl8_5
| ~ spl8_6 ),
inference(avatar_split_clause,[],[f443,f65,f62]) ).
cnf(s1,plain,
( spl8_1
| spl8_2 ),
inference(sat_conversion,[],[f49]) ).
cnf(s2,plain,
( spl8_2
| spl8_3 ),
inference(sat_conversion,[],[f54]) ).
cnf(s3,plain,
( spl8_1
| spl8_4 ),
inference(sat_conversion,[],[f59]) ).
cnf(s4,plain,
( spl8_3
| spl8_4 ),
inference(sat_conversion,[],[f60]) ).
cnf(s5,plain,
( spl8_5
| spl8_6 ),
inference(sat_conversion,[],[f67]) ).
cnf(s11,plain,
( ~ spl8_2
| ~ spl8_4
| ~ spl8_5 ),
inference(sat_conversion,[],[f307]) ).
cnf(s13,plain,
( ~ spl8_2
| ~ spl8_4
| ~ spl8_6 ),
inference(sat_conversion,[],[f337]) ).
cnf(s15,plain,
( ~ spl8_1
| ~ spl8_3
| ~ spl8_5 ),
inference(sat_conversion,[],[f404]) ).
cnf(s16,plain,
( spl8_5
| ~ spl8_6 ),
inference(sat_conversion,[],[f444]) ).
cnf(s19,plain,
( ~ spl8_2
| ~ spl8_4 ),
inference(rat,[],[s5,s13,s11]) ).
cnf(s20,plain,
spl8_1,
inference(rat,[],[s19,s1,s3]) ).
cnf(s21,plain,
spl8_5,
inference(rat,[],[s5,s16]) ).
cnf(s22,plain,
~ spl8_3,
inference(rat,[],[s15,s20,s21]) ).
cnf(s23,plain,
spl8_4,
inference(rat,[],[s4,s22]) ).
cnf(s24,plain,
spl8_2,
inference(rat,[],[s2,s22]) ).
cnf(s25,plain,
$false,
inference(rat,[],[s19,s23,s24]) ).
thf(f453,plain,
$false,
inference(avatar_sat_refutation,[],[s25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV465^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.18 % Computer : n008.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 15:49:54 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 Running first-order model finding
% 0.08/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.32 % (3328906)Will run a generic schedule for satisfiability detection.
% 0.19/0.32 % (3328915)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1716737022:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.32 % (3328915)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.32 % (3328912)% WARNING: option uhcvi not known.
% 0.19/0.32 % (3328911)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1746405717_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.32 % (3328913)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2323601810:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.32 % (3328914)dis+10_1_sil=32000:sp=arity:random_seed=3229837075:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.32 % (3328912)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2322429487:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.32 % Exception at run slice level
% 0.19/0.32 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.32 % (3328912)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.32 % (3328912)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.19/0.32 % (3328917)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1492993361:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.32 % (3328916)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4155447431:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.32 % (3328924)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1932490263:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.19/0.32 % Exception at run slice level
% 0.19/0.32 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.32 % (3328915)Instruction limit reached!
% 0.19/0.32 % (3328915)------------------------------
% 0.19/0.32 % (3328915)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.32 % (3328915)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.32 % (3328915)CaDiCaL version: 2.1.3
% 0.19/0.32 % (3328915)Termination reason: Instruction limit
% 0.19/0.32 % (3328915)Termination phase: Saturation
% 0.19/0.32 % (3328915)Time elapsed: 0.037 s
% 0.19/0.32 % (3328915)Peak memory usage: 13 MB
% 0.19/0.32 % (3328915)Instructions burned: 116 (million)
% 0.19/0.32 % (3328928)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=3919748637:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.19/0.32 % (3328928)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.32 % (3328928)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.19/0.32 % (3328927)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3667580813:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.32 % (3328912) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3328906-3328912"...
% 0.19/0.32 % (3328912)...printing done.
% 0.19/0.32 % (3328912)Refutation found. Thanks to Tanya!
% 0.19/0.32 % SZS status Theorem for theBenchmark
% 0.19/0.32 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.32 % (3328912)------------------------------
% 0.19/0.32 % (3328912)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.32 % (3328912)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.32 % (3328912)CaDiCaL version: 2.1.3
% 0.19/0.32 % (3328912)Termination reason: Refutation
% 0.19/0.32 % (3328912)Time elapsed: 0.053 s
% 0.19/0.32 % (3328912)Peak memory usage: 13 MB
% 0.19/0.32 % (3328912)Instructions burned: 93 (million)
% 0.19/0.32 % (3328906)Success in time 0.095 s
% 0.19/0.32 % Vampire exiting
%------------------------------------------------------------------------------